相关论文: A non commutative sewing lemma
We prove the non-commutative Laurent phenomenon for two variables.
In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…
There have been comments on the starting paper, hep-th/0106074, which point out unclear motivation and definitions on noncommutative momentum introduced. Thus, this paper is withdrawn by the author for more clear presentation.
In this article, following an insight of Kontsevich, we extend the famous Weil conjecture (as well as the strong form of the Tate conjecture) from the realm of algebraic geometry to the broad noncommutative setting of dg categories. As a…
This paper is the sequel of the paper "Continuity of volumes on arithmetic varieties", in which we established the arithmetic volume function of smooth hermitian Q-invertible sheaves and proved its continuity. The continuity of the volume…
In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma…
The paper provides a version of the rational Hodge conjecture for $\3\dg$ categories. The noncommutative Hodge conjecture is equivalent to the version proposed in \cite{perry2020integral} for admissible subcategories. We obtain examples of…
Koopman operator theory and Willems' fundamental lemma both can provide (approximated) data-driven linear representation for nonlinear systems. However, choosing lifting functions for the Koopman operator is challenging, and the quality of…
This is an expository article on the noncommutative singularity theory of power series in noncommuting variables, its motivation from deformation theory, and its applications to contractibility of curves and the classification of smooth…
We investigate the geode and some of its generalizations from the point of view on noncommutative symmetric functions.
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a…
Peak interpolation is concerned with a foundational kind of mathematical task: building functions in a fixed algebra $A$ which have prescribed values or behaviour on a fixed closed subset (or on several disjoint subsets). In this paper we…
We present a constructive proof of Brouwer's fixed point theorem for uniformly continuous and sequentially locally non-constant functions based on the existence of approximate fixed points. And we will show that Brouwer's fixed point…
We prove conjectures of the third author [L. Tevlin, Proc. FPSAC'07, Tianjin] on two new bases of noncommutative symmetric functions: the transition matrices from the ribbon basis have nonnegative integral coefficients. This is done by…
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
Galois closures of commutative rank n ring extensions were introduced by Bhargava and the second author. In this paper, we generalize the construction to the case of non-commutative rings. We show that non-commutative Galois closures…
A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…
There have been comments on the starting paper, hep-th/0106074, which point out unclear motivation and definitions on noncommutative momentum introduced. This paper is withdrawn by the author for more clear presentation.
We explicitly derive, following a Noether-like approach, the criteria for preserving Poincare invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that,…